Predicting productivity loss caused by change orders using the evolutionary fuzzy support vector machine inference model

  Journal of Civil Engineering and Management

  ISSN: 1392-3730 (Print) 1822-3605 (Online) Journal homepage: Predicting productivity loss caused by change

orders using the evolutionary fuzzy support vector

machine inference model Min-Yuan Cheng, Dedy Kurniawan Wibowo, Doddy Prayogo & Andreas F. V. Roy

To cite this article: Min-Yuan Cheng, Dedy Kurniawan Wibowo, Doddy Prayogo & Andreas F. V.

  Roy (2015) Predicting productivity loss caused by change orders using the evolutionary fuzzy support vector machine inference model, Journal of Civil Engineering and Management, 21:7, 881-892, DOI: To link to this article: Published online: 10 Jul 2015.

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JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT

  ISSN 1392-3730 / eISSN 1822-3605 2015 Volume 21(7): 881–892 doi:10.3846/13923730.2014.893922

PREDICTING PRODUCTIVITY LOSS CAUSED BY CHANGE ORDERS USING THE EVOLUTIONARY FUZZY SUPPORT VECTOR MACHINE

  a, b , Doddy PRAYOGO a

  Changes during construction projects are very common, making construction one of the most complex industries. Changes can involve adding to or reducing the scope of project work or correcting or modifying an original design. Change orders in the construction industry have negative effects in aspects such as cost, quality, time, and organization. While most change order items (e.g. mate- rial, scheduling, rework, equipment) can be relatively easy to measure, quantifying the impact on labor produc- tivity is typically more complicated (Hanna et al. 1999a).

  , Dedy Kurniawan WIBOWO

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  Several AI hybrid systems have been developed in recent years that have solved various construction man- agement problems (Cheng, Wu 2009; Cheng, Roy 2010).

  Construction projects are complex undertakings full of uncertainty and vagueness. Developing a determin- istic mathematical model to predict productivity loss is difficult and expensive. An inference model (Cheng, Wu 2009) offering high accuracy and low cost is one fea- sible approach to predicting productivity loss. Inference models derive new facts from historical data. The human brain can learn previous information and deduce new facts from that information. Artificial intelligence (AI) can be employed to develop models that simulate human brain functions. AI is concerned with computer systems able to handle complex problems using techniques such as Artificial Neural Network (ANN), Support Vector Machine (SVM), and Fuzzy Logic (FL). AI-based infer- ence models thus offer a promising solution to predicting productivity loss.

  1991; Ibbs 2005), (2) artificial neural network (ANN) (Moselhi et al. 2005), and (3) statistical- fuzzy (Hanna et al. 2002). Previous studies (Hanna et al. 2002; Moselhi et al. 2005) have reported that ANN and statistical-fuzzy methods outperform regression analy- sis. However, no method is suitable for calculating productivity loss because prediction accuracies are out- side of acceptable limits.

  Many studies have reported on the impact of change orders on labor productivity. The methods used in the literature to calculate productivity loss can be grouped into the 3 categories of (1) regression analysis (Leonard 1988; Moselhi et al.

  Corresponding author: Doddy Prayogo E-mail: doddyprayogo@ymail.com Introduction

  , Andreas F. V. ROY c a

  Min-Yuan CHENG a

  Abstract. Change orders in construction projects are very common and result in negative impacts on various project facets. The impact of change orders on labor productivity is particularly difficult to quantify. Traditional approaches are inadequate to calculate the complex input-output relationship necessary to measure the effect of change orders. This study develops the Evolutionary Fuzzy Support Vector Machines Inference Model (EFSIM) to more accurately predict change-order-related productivity losses. The EFSIM is an AI-based tool that combines fuzzy logic (FL), support vector machine (SVM), and fast messy genetic algorithm (fmGA). The SVM is utilized as a supervised learning technique to solve classification and regression problems; the FL is used to quantify vagueness and uncertainty; and the fmGA is ap- plied to optimize model parameters. A case study is presented to demonstrate and validate EFSIM performance. Simula- tion results and our validation against previous studies demonstrate that the EFSIM predicts the impact of change orders significantly better than other AI-based tools including the artificial neural network (ANN), support vector machine (SVM), and evolutionary support vector machine inference model (ESIM).

  Received 07 Dec 2012; accepted 19 Feb 2013

  Department of Civil Engineering, Faculty of Engineering, Parahyangan Catholic University, Jalan Ciumbuleuit 94, Bandung, 40141 West Java, Indonesia

  Department of Civil Engineering, Sepuluh Nopember Institute of Technology, Nopember, Indonesia c

  Department of Civil and Construction Engineering, National Taiwan University of Science and Technology, #43, Sec. 4, Keelung Rd., Taipei, Taiwan, R. O.C. b

  Keywords: change orders, productivity loss, fuzzy logic, support vector machine, fast messy genetic algorithm.

  M.-Y. Cheng et al. Predicting productivity loss caused by change orders using the evolutionary fuzzy support vector ...

  The advantages of FL related to vagueness and uncertainty depend heavily on the appropriate distribution of membership functions (MFs), number of rules, and selection of proper fuzzy set operations. Greater problem complexity increases the difficulty of MF construction and rules (Ko 2002). Some researchers have treated this drawback as an optimization problem because determin- ing MF configurations and fuzzy rules is complicated and problem-oriented. To overcome such difficulties, some researchers have tried to fuse FL with AI optimization techniques such as GA and ant colony (Ishigami et al. 1995; Martinez et al. 2008) . These optimization meth- ods have demonstrated their ability to minimize time- consuming operations and reduce the level of human intervention necessary to optimize MFs and fuzzy rules.

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  SVM has achieved performance levels compara-

  ). A radial basis function (RBF) kernel has been recommended for general users as a first choice due to its ability to analyze higher-dimension data, use of only one hyperparameter in searches, and fewer numerical dif- ficulties (Hsu et al. 2003).

  j

  , x

  i

  SVM (Vapnik 1995) is an AI paradigm already used in a wide range of applications. SVM is a learning tool for solving classification and regression problems. SVM works by plotting input vectors into a higher dimensional feature space. The optimal hyperplane is identified within this feature space with the help of a kernel function, K (x

  1.3. Support vector machine (SVM)

  The result of fuzzification, which is used by the inference engine, stimulates the human decision–making process based on fuzzy implications and available rules. Lastly, defuzzification reverses the fuzzification process and converts the fuzzy set into crisp output.

  In an AI hybrid system, fusing different AI techniques can achieve better results than a single AI technique because the advantages of one technique can compen- sate for another’s disadvantages (Cheng, Wu 2009). The Evolutionary Fuzzy Support Vector Machine Inference Model (EFSIM) (Cheng, Roy 2010) was proposed to further improve prediction accuracy. EFSIM is an arti- ficial intelligence (AI) hybrid system that fuses fuzzy logic (FL), support vector machine (SVM), and fast messy genetic algorithm (fmGA). In EFSIM, FL deals with vagueness and uncertainty; SVM acts as a super- vised learning tool; and fmGA works to optimize FL and SVM parameters. EFSIM significantly reduces the level of human intervention and can be used by professionals who do not have background in AI (Cheng, Roy 2010).

  FL is a popular AI technique invented by Zadeh in the 1960s. FL has been used in forecasting, decision mak- ing, and action control in environments characterized by uncertainty, vagueness, presumptions, or subjectivity (Bojadziev, G., Bojadziev, M. 2007). In general, FL sys- tems have four major components: fuzzification, fuzzy rule base, inference engine, and defuzzification. Fuzzifi- cation is a process that uses membership functions (MFs) to convert the value of each input variable into a corre- sponding linguistic variable degree. Fuzzy rules repre- sent relations between input and output fuzzy sets and form the basis for fuzzy logic to obtain fuzzy output.

  1.2. Fuzzy logic (FL)

  A neural network model (Moselhi et al. 2005) was developed to estimate the impact of change orders on labor productivity, including the timing effect of change orders. Analysis results showed this model estimated the impact of change orders on productivity more accurately than those previously described. However, this method could gain better prediction results by fusing the neural network model with an AI technique.

  an efficiency indicator and regression analysis to ana- lyze questionnaire data. Hanna et al. (2002) improved the method by using the statistical-fuzzy technique to quantify the cumulative impact of change orders. Unfor- tunately, the technique is difficult for stakeholders to implement due to complicated calculation steps and poor

  et al. 1999a, b). These studies used the delta method as

  Two studies used a statistical method to quantify the impact of change orders on labor productivity in mechanical and electrical construction projects (Hanna

  Preliminary research into calculating the effects of change orders on labor productivity was accomplished by Leonard (1988). This research attempted to identify the effects of change orders on labor productivity in 90 cases facing change-order-related productivity losses. Results indicated a significant correlation between change orders and productivity loss. However, there were limitations to Leonard’s study, including limited number of variables and subjective evaluation (Hanna et al. 1999a, b). This preliminary study motivated other researchers to develop research in this field further.

  Change can be defined as any modification in the original scope, time, or cost of the work (Hester et al. 1991). A change order is issued to formally announce the change and modify the contract between the contractor and owner (Hester et al. 1991). Keane et al. (2010) grouped causes of change into four categories: owner-related, consultant-related, contractor-related, and non-party- related, and effects of change into five categories: cost-related, quality-related, time-related, organization- related, other effects (Keane et al. 2010).

  The objective of this research is to use EFSIM to predict productivity loss caused by change orders. Fea- sibility and capability of the proposed method are evalu- ated and compared with other methods, including ANN, SVM, and ESIM (Cheng, Wu 2009). Validation with pre- vious studies (Moselhi et al. 2005) is also carried out to demonstrate proposed model performance.

1. Literature review

1.1. Productivity loss caused by change orders

  Journal of Civil Engineering and Management, 2015, 21(7): 881–892

  1998; Yongqiao et al. 2005). However, SVM’s generali- zation ability and prediction accuracy are determined by the optimal penalty (C

  ) and kernel (γ) parameters. To overcome this drawback, an optimization technique (e.g. fmGA) may be used to identify the optimum values of parameters simultaneously (Cheng, Wu 2009).

1.4. Fast messy genetic algorithm (fmGA)

  fmGA is a recently developed machine learning and optimization tool based on a genetic algorithm approach (Goldberg et al. 1993). fmGA is an improvement on messy genetic algorithms (mGAs), which were initially developed to overcome linkage problems in simple genetic algorithms (sGAs) resulting from a parameter coding problem that sometimes generates suboptimal solutions (Deb, Goldberg 1991). Unlike sGAs, which use fixed length strings to represent possible solutions, fmGA applies messy chromosomes to form strings of various lengths that can efficiently find optimal solutions for large-scale permutation problems (Feng, Wu 2006).

  The fmGA contains two loop types: inner and outer (Fig. 1). The process starts with the outer loop. Firstly, a competitive template (randomly generated or problem- specific) is generated. In the inner loop, the fmGA oper- ation is three-phase, including an initialization phase, primordial phase, and juxtapositional phase. In the initialization phase, an adequately large population con- tains all possible building blocks (BBs) of order k. fmGA performs the probabilistic complete initialization (PCI) by generating n chromosomes randomly and evaluat- ing their fitness value. The primordial phase contains two operations, namely threshold selection and build- ing-block filtering. In this phase, “bad” genes that do not belong to BBs are filtered out so that, in the end, the result encloses a high proportion of “good” genes belonging to BBs. In the juxtapositional phase, fmGA operations are similar to sGA operations. The selection for “good” genes is used together with a cut-and-splice operator to form a high-quality generation that may con- tain the optimal solution. The next outer loop begins after the respective inner loop is finished. The competi- tive template is replaced by the best solution found so far, which becomes the new competitive template for the next outer loop. The whole process is performed until the

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  M.-Y. Cheng et al. Predicting productivity loss caused by change orders using the evolutionary fuzzy support vector ...

  maximum number of eras (k

  max

  ) is reached. The fmGA can also be performed over epochs (e

  max

  ). An epoch is the complete process between first era and the maxi- mum number of eras (k

  max

  ). Epochs can be performed as many times as desired. The algorithm is terminated once a good-enough solution is obtained or no further improvement is made.

  This study used the Summit and Width Representation Method (SWRM) (Ko 2002) to encode complete MF sets (Fig. 3 (c)). Figure 4 illustrates the fuzzification process.

  2) Fuzzification Each normalized input attribute from the previous step is converted into membership grades corresponding to the specific membership function (MF) set generated and encoded by fmGA. This model uses trapezoidal and triangular MF shapes (see Fig. 3) that, in general, may be developed by referencing summit points and widths.

2. Evolutionary fuzzy support vector machine inference model

  1) Training data Final data for training are obtained from data pre- processing output. Data preprocessing used in this study included data cleaning, attribute reduction and data trans- formation.

  In EFSIM, the fuzzy inference engine and fuzzy rules based on the FL system have been replaced by SVM. However, SVM’s generalization ability and prediction accuracy are determined by the optimal penalty (C) and kernel (γ) parameters. Improper tuning of the parameters will affect the accuracy of the prediction model. To over- come this shortcoming, EFSIM utilizes fmGA to search simultaneously for optimum SVM parameters and FL parameters. The architecture of EFSIM is shown in Figure 2.

  The evolutionary fuzzy support vector machine infer- ence model (EFSIM) is a hybrid AI system developed by Cheng and Roy (2010) that fuses the three different AI techniques of fuzzy logic (FL), support vector machine (SVM), and fast messy genetic algorithm (fmGA). In this complementary system, FL deals with vagueness and approximate reasoning; SVM acts as a supervised learning tool to handle fuzzy input-output mapping; and fmGA works to optimize FL and SVM parameters.

  3) SVM training model SVM addresses the complex relationship between fuzzy input and output variables. Fuzzification process output, in the form of membership grades, is fuzzy input for SVM. SVM trains the dataset to obtain the prediction model, with penalty (C

  ) and kernel (γ) as its parameters, which are randomly generated and encoded by fmGA. This study used the RBF kernel as a reasonable first choice (Hsu et al. 2003).

  4) Defuzzification This is a fuzzification reverse process. Once

  SVM finishes the training process, output numbers are expressed in terms of a fuzzy set. Output numbers are then converted into crisp numbers. Employing fmGA, the model generates a random defuzzification parameter (dfp) substring and encodes it for conversion into SVM fuzzy output. This evolutionary approach is simple and straightforward, as it uses dfp as a common denominator for SVM output.

  5) fmGA parameter search fmGA is utilized to search simultaneously the fittest shapes for MFs, dfp, penalty parameter (C), and RBF kernel parameter (γ). In fmGA, the chromosome that represents the possible solution for searched parameters consists of four parts: the MFs substring, dfp substring, penalty parameter substring, and kernel parameter sub- string (Cheng, Roy 2010). The chromosome is encoded into a binary string. Chromosomes consist of two seg- ments: FL and SVM. Figure 5 illustrates the chromosome

  Fig. 2. Architecture of EFSIM Downloaded by [NATIONAL TAIWAN UNIVERSITY OF SCIENCE AND TECHNOLOGY], [Doddy Prayogo] at 00:51 11 November 2015

  The EFSIM involves eight major steps, beginning with training data and ending with the optimal prediction model. An explanation of major steps involved in EFSIM is given below:

  Journal of Civil Engineering and Management, 2015, 21(7): 881–892

  6) Fitness evaluation A fitness function, a function designed to measure model accuracy and good generalization properties (Ko

  Fig. 3. Membership function: trapezoidal (a), triangular (b), complete MF set (c) (Ko 2002) Fig. 4. Fuzzification process

  represents the prediction error between actual output

  s er

  represents the accuracy weighting coefficient;

  aw

  (1) where c

  number, and SVM parameters. The fitness function consists of parameters to calculate accuracy and model complexity, as expressed in Eqn (1):

  dfp

  2002), is now developed to evaluate fitness value. This function describes the fittest shape of MFs, optimized

  9 a Number of bits required for one complete MF set.

  structure. Table 1 summarizes the parameter settings and number of bits required for the chromosome design. For more details about fmGA parameter search, readers are referred to the previous work of Cheng and Wu (2009)

  0.5

  1

  10 dfp

  1 0.0001

  5 γ

  C 200

  27 a

  Number of bits MF set – –

  Fig. 5. EFSIM chromosome structure Table 1. Summary of EFSIM parameter settings Parameter Upper bound Lower bound

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  M.-Y. Cheng et al. Predicting productivity loss caused by change orders using the evolutionary fuzzy support vector ...

  and desired output; c

  cw

  represents the complexity weight- ing coefficient; and mc represents model complexity, which can be quantified by counting the number of sup- port vectors.

  7) Termination criteria The process terminates when the termination crite- rion is satisfied. While still unsatisfied, the model will proceed to the next generation. As EFSIM uses fmGA, the termination criterion used in this study was either era number (k) or epoch number (e).

  8) Optimal prediction model The loop stops when the termination criterion is fulfilled. This condition means that the prediction model has identified the input/output mapping relationship with optimal C, γ, and dfp parameters and is ready to predict new facts.

3. Productivity loss prediction using EFSIM

  Data used in this research were drawn from 102 cases cited in Assem’s thesis (2000) and covered 33 cases from Assem’s (2000) investigation of the adverse effects of change orders and 69 cases from Leonard’s (1988) inves- tigation of change order impacts. A summary of cases is shown in Table 2.

  is the maxi- mum data.

  Fig. 6. Flowchart of data preprocessing Downloaded by [NATIONAL TAIWAN UNIVERSITY OF SCIENCE AND TECHNOLOGY], [Doddy Prayogo] at 00:51 11 November 2015

  1 represents change-order causes of productivity loss only; 2 or 3 represents change order plus 1 or 2 additional major causes of productivity loss.

  0.006 0.573 0.198 Type of impact (1, 2, or 3) c a frequency of change order: ratio change orders number to the actual duration in months; b average size of change orders: ratio of change orders hours to the number of change orders; c

  3.214 1595.238 161.964 Change orders hours 100 83000 10528.688 Change orders hours ratio to the planned hours 0.009 2.660 0.323 Change orders hours ratio to the actual hours

  7 2150 106.784 Frequency of change orders a 0.389 195.454 8.614 Average size of change orders b

  Work type (Architectural, Civil, Electrical, Mechanical) Change orders number

  Table 2. Summary cases Parameter Min Max Mean

  A total of 96 records were used to train the prediction model. Two kinds of analyses were done to compare performance of attribute reduction methods. Analysis 1 used CA to reduce attributes and Analysis 2 used PCA to do the same. As shown in Table 3, CA and PCA identi- fied 6 and 4 attributes, respectively, as significant factors. Both analyses transformed the data into values ranging

  3.3. Final data

  max

  3.2. Data preprocessing

  is the minimum data; and x

  min

  3.1. Historical data

  i

  is the normalized data; x

  norm

  , (2) where: x

  Data cleaning can be applied to fill in missing values and remove noisy data (univariate and multivariate out- liers) (Han, Kamber 2007; Shahi et al. 2009). Attributes reduction was applied to reduce the dimensionality of data attributes and help reduce computational time by eliminat- ing unnecessary attributes. Two methods, correlation anal- ysis (CA) and principal component analysis (PCA), were employed to compare attributes reduction method results. CA is the simplest way to assess input-output relationships. PCA is used to identify strong predictor variables in a data- set. Data transformation techniques such as normalization, where attribute data are scaled to fall within a small speci- fied range, may improve the accuracy and the efficiency of mining algorithms involving distance measurements (Han, Kamber 2007; Shahi et al. 2009). The function used to normalize data in this study is shown in Eqn (2):

  Data preprocessing is an important stage in data analy- sis that resolves the “unclean” nature of real-world data (Zhang et al. 2003). Several data preprocessing tech- niques such as data cleaning, attributes reduction, and data transformation were employed in this study. A systematic data-preprocessing flowchart (Fig. 6) was developed to obtain better prediction results. Historical data was ana- lyzed using this flowchart to obtain training data.

  is the observed data; x

  Journal of Civil Engineering and Management, 2015, 21(7): 881–892 Table 3. Summary of training data

  were used for training (Fig. 7). We then calculated the average of each performance measure to obtain cross-

  Analysis 1 (CA) Analysis 2 (PCA) validation accuracy. Work type Work type Frequency of change orders Type of impact

  3.5. Performance measures tes

  This research used the following four performance meas-

  Average size of change Frequency of change

  orders orders

  ures to evaluate EFSIM:

  attribu Change order hours Time related 1.

  Root mean square error

  Change order hours ratio to Relative size of change

  Root mean square error (RMSE) is the square root

  the planned hours orders

  of the average squared distance of predicted values by

  Change order hours ratio to

  the model and the observed values. RMSE can be used

  Significant the actual hours

  to calculate the variation of errors in a prediction model and is very useful when large errors are undesirable. The between 0 and 1. Table 4 shows example input and out- RMSE is expressed using the following equation: put data from Analysis 1.

  (3)

3.4. Cross-validation

  Cross-validation is a statistical technique that assesses how accurately a predictive model will perform by divid- where y is the actual value; is the predicted value; and

  j

  ing data into two segments, of which one is used to learn n is the number of data samples. or train the model and the other is used to test or validate

  2. Mean absolute error the model. 10-fold cross-validation resulted in the best Mean absolute error (MAE) is the average absolute performance in the simulation (Borra, Di Ciaccio 2010). value of the residual (error). MAE is a quantity used to

  In 10-fold cross-validation, original data was randomly measure how close forecasts or predictions are to even- portioned into 10 equally (or approximately equally) sized tual outcomes. The MAE is expressed using the follow- segments. Consequently, 10 independent performance ing equation: estimations of training and testing were performed such that, within estimation, a different fold of the data was

  (4) alternately used for testing while the remaining 9 folds

  Table 4. Input and output data for Analysis 1 No. Actual % Average size Change order Change order Change order Work type Frequency productivity hours hours/planned hours/actual loss hours hours

  1

  23.7 1 1.54545 33.41176 568 0.08686 0.06494

  2

  24.5 1 1.36000 165.02941 5611 0.11567 0.08492

  3

  31.8 1 1.20000 69.75000 837 0.13368 0.08745

  4

  11 3 9.75000 25.35897 989 0.08074 0.07122

  5

  27 3 0.47619 138.80000 1388 0.68850 0.42382

  6

  19 3 1.81818 71.15625 5692.5 0.12291 0.09728 … … … … … … … …

  41

  18.4 2 12.04762 129.64427 32800 0.41362 0.33745

  42

  22.81 2 21.11111 113.15789 21500 0.48864 0.37719

  43

  14.18 2 0.80000 191.66667 2300 0.10000 0.08582

  44

  17.75 2 0.73333 272.72727 3000 0.05769 0.04745

  45

  19.03 2 0.71429 190.00000 1900 0.13333 0.10795

  46

  21.05 2 6.25000 189.33333 14200 0.13524 0.10677 … … … … … … … … Downloaded by [NATIONAL TAIWAN UNIVERSITY OF SCIENCE AND TECHNOLOGY], [Doddy Prayogo] at 00:51 11 November 2015

  92

  38.71 4 34.00000 135.29412 23000 0.68047 0.39792

  93

  44.31 4 4.64286 61.53846 4000 0.66116 0.53121

  94

  48.95 4 6.47059 156.36364 17200 1.01176 0.51652

  95

  35.09 4 2.42857 63.23529 4300 0.11406 0.07713

  96

  45.34 4 2.92857 336.58537 13800 0.31364 0.17143

  M.-Y. Cheng et al. Predicting productivity loss caused by change orders using the evolutionary fuzzy support vector ...

  4. Results and discussion

  4.1. Model performance

  A systematic methodology was previously established to calculate prediction performance. Database records contain several attributes related to productivity loss caused by change orders. Data preprocessing was done to improve data quality. In the data preprocessing stage, two kinds of analysis relate to attributes reduction meth- ods. We performed Analyses 1 and 2 to compare the per- formance of each. Analysis 1 employed the CA method and Analysis 2 employed the PCA method, with each implementing training and testing processes in accord- ance with 10-fold cross-validation.

  In the testing process, each fold validates the perfor- mance of the proposed model. A comparison with other methods such as ESIM (Cheng, Wu 2009), ANN, and SVM was developed to show EFSIM as more accurate and reliable. Several performance measures (RMSE, MAE, MAPE, and training time) were employed to eval- uate the proposed model.

  Table 5 summarizes our comparison of Analyses 1 and 2 results. Optimal EFSIM parameter of Analysis 1 is

  Fig. 7. 10-fold cross-validation

  C = 31 and γ = 0.574, founded in fold 3. Meanwhile, C = 31 and γ = 0.566 of fold 9 is regarded as the optimal EFSIM parameter in Analysis 2. In Analysis 1 earned

  3. Mean absolute percentage error better results in all EFSIM and ESIM performance meas- Mean absolute percentage error (MAPE) is a meas- ures except for MAPE. On the other hand, Analysis 2 urement of prediction accuracy. It represents prediction obtained better results in SVM and ANN. Analysis 1 had percentage error. Small denominators can cause problems a higher EFSIM training time than Analysis 2 because of in MAPE value because small denominators generate its larger number of attributes. large MAPE values that impact overall value. The MAPE

  However, the difference between the two analyses is expressed using the following equation: in terms of the MAPE performance measure was not sig- nificant. Table 5 shows EFSIM results found both Analy- sis 1 and Analysis 2 to be significantly more accurate

  (5) than other AI techniques. Longer computation time is required for the EFSIM model due to the FL paradigm. The more attributes in a training process, the more train-

  4. Training time ing time is needed to obtain the prediction model.

  Training time represents time taken by the proposed Table 6 shows average Analysis 1 and 2 perfor- model to train data and obtain the optimum prediction mance values. The best model with the smallest RMSE model. value is EFSIM (2.98%). Moreover, Table 6 shows a

  To obtain an overall comparison, a normalized refer- ence index (RI) (Chou et al. 2011) was created by com- bining the four performance measures (RMSE, MAE, and

  Table 5. Performance of predictive techniques for Analyses 1 and 2

  MAPE, and training time). The RI was obtained by calcu- lating the average of each normalized performance meas-

  Average Predictive RMSE MAE MAPE

  ure. Performance measure values ranged from 1 (best) to 0

  Analysis training (%) (%) (%) technique time (s)

  (worst). The equation of RI can be described as follows:

  EFSIM

  2.83

  2.25 30.44 7065.73 ESIM

  6.57

  5.62 55.40 231.3

  (6) ANN

  9.24

  8.00

  76.43

  1 Downloaded by [NATIONAL TAIWAN UNIVERSITY OF SCIENCE AND TECHNOLOGY], [Doddy Prayogo] at 00:51 11 November 2015 Analysis 1

  SVM

  9.12

  7.78

  60.70

  1

  where: x is the measurement indicator (RMSE, MAPE,

  i EFSIM

  3.13

  2.51 23.85 5146.83

  MAE, training time); is the maximum value of the

  ESIM

  7.12

  6.07 48.12 138.2

  indicator among all prediction methods; is the mini-

  ANN

  8.79

  7.55

  72.82

  1

  mum value of the indicator among all prediction meth-

  Analysis 2 SVM

  8.61

  7.23

  65.16

  1

  Journal of Civil Engineering and Management, 2015, 21(7): 881–892

  direct relationship between RMSE and MAE. MAE In terms of training time, both ANN and SVM train data values are always smaller than RMSE values. EFSIM relatively quickly, while ESIM requires more time and obtains the smallest MAE value (2.38 %) of all models.

  EFSIM requires the most time. This is due to the FL par- MAPE values are inadequate in all models due to the adigm that requires more computational time during the series of small denominator values. MAPE values are training process and to the status of ESIM and EFSIM consistent with other performance measures (RMSE and as hybrid AI techniques. Longer computational time is a MAE). The best model is obtained by EFSIM (27.15%). trade off necessary to obtain greater accuracy. Figure 8 illustrates the performance described in Table 6.

  The normalized RI obtained a general measure-

  Table 6. Average performance values of the predictive techniques

  ment by combining all performance measures. Based on RI values, EFSIM is the best model, followed in order

  Average Predictive RMSE MAE MAPE

  by ESIM, SVM, and ANN. Although EFSIM requires

  training RI (%) (%) (%) technique

  the longest training time, it consistently obtains the best

  time (s)

  results on most other performance measures. Thus, by

  EFSIM

  2.98

  2.38 27.15 6106.28 0.7500

  fusing FL, SVM, and fmGA, EFSIM predicts change-

  ESIM

  6.84

  5.84 51.76 184.75 0.5423

  order-related productivity loss more accurately than the

  ANN

  9.01

  7.77

  74.62 1 0.2500 other models considered. SVM

  8.86

  7.70

  62.93 1 0.3303 Downloaded by [NATIONAL TAIWAN UNIVERSITY OF SCIENCE AND TECHNOLOGY], [Doddy Prayogo] at 00:51 11 November 2015

  Fig. 8. Average result for performance measures with 10-fold cross-validation

  M.-Y. Cheng et al. Predicting productivity loss caused by change orders using the evolutionary fuzzy support vector ...

4.2. Validation with previous studies

  et al. 1991), electrical regression model (Hanna et al.

  30.00

  44.51 1,467 7.91 1,240 22.16 1,749 –9.78 4 1,741 2,070 –18.90 2,041 –17.23 2,674 –53.59 1,799 –3.32 5 2,660 1,744 34.44 2,966 –11.50 2,699 –1.47 2,550

  4.14 6 5,139 N/A N/A 2,485 51.64 5,078a 1.19 4,912

  4.42 7 13,713 11,469 16.36 10,644 22.38 15,169 –10.62 13,822 –0.79 8 10,575 5,073 52.03 2,438 76.95 7,077 33.08 8,350

  21.04 Average error c

  (%)

  30.45

  40.50

  17.83

  7.90 Average absolute error d

  (%)

  25.30

  19.44

  Estimating error b

  6.24 Notes: N/A = not applicable (i.e. off model range); a

  Two additional types of impact are considered in the estimate (i.e. TI = 3); b

  Estimating error j

  = _j ^{j j} Actual loss Estimated loss loss Actual ) ( −

  , where j represents case 1 to 8; c

  Average error = ∑ ∑

  = = − _{8 1} ⁸ ₁ | | _{j j j j j}

  Actual loss Estimated loss loss Actual ; d

  Average absolute error =

  8 | | ⁸ ₁ ∑ = ^{j j}

  Estimated loss .

  Downloaded by [NATIONAL TAIWAN UNIVERSITY OF SCIENCE AND TECHNOLOGY], [Doddy Prayogo] at 00:51 11 November 2015

  (%) 1 801 731 8.74 650 18.85 940 –17.35 822 –2.68 2 1,073 1,050a 2.14 713 33.55 1,245a –16.03 1,113 –3.75 3 1,593 884

  (%) Estimated productivity loss (h)

  1999b), and neural network model (Moselhi et al. 2005). Our validation used a dataset of 33 records from Assem (2000) as training data and change-order data from the literature (Bruggink 1997) as testing data. Attributes used in this dataset were (1) timing impact of change orders (TP

  The cases were analyzed using EFSIM and results were compared with previous studies found in Moselhi

  i

  ); (2) work type; and (3) type of impact (TI), which could be either change orders only or change orders plus 1 or 2 additional causes of productivity related impact. TP

  i

  represents the ratio of actual change order hours to planned hours in each of the five construction periods (i = 1 to 5) as shown in following equation:

  (7) where: TP

  i

  is the timing impact of change orders in period i;

  HCO i

  is the actual change order hours during period i; PH

  i

  is the planned hours during period i; and i is the period when change orders occur, where the value of i can range from 1 to 5. This data set used NECA (1983) distribution for electrical work and the trapezoidal distribution of Bent and Thuman (1994) for other types of work to distribute the planned hours in each of the five construction periods.

  et al. (2005). Table 7 shows comparisons among all

  We compared the performance of EFSIM against other methods such as the general regression model (Moselhi

  methods. Results demonstrate that the EFSIM model pro- posed in this study outperforms all other models in terms of estimating the impact of change orders on productiv- ity. EFSIM obtained the smallest average error (7.90%) and lowest average absolute error of any model. This shows that EFSIM improves prediction model accuracy and reliability.

  Conclusions

  This research proposes a hybrid AI technique, EFSIM, to predict productivity loss caused by change orders. The EFSIM, developed by fusing complementary AI tech- niques including FL, SVM, and fmGA, achieves predic- tion results superior to traditional techniques.

  The developed model reduces the level of human intervention necessary to elicit MF shapes from question- naire surveys and expert judgment; it also successfully identifies optimum penalty and kernel parameters. EFSIM is easy to apply and convenient for new users, and may be used by professionals without AI domain knowledge.

  Test results show that EFSIM prediction perfor- mance is superior to other prediction methods such as ESIM, ANN, and SVM. Although EFSIM requires

  Table 7. Actual versus estimated productivity loss (Moselhi et al. 2005) Case No.

  (j) Actual productivity loss (h)

  Moselhi et al. (1991) Hanna et al. (1999) Moselhi et al. (2005) Proposed model (EFSIM) Estimated productivity loss (h)

  Estimating error b

  (%) Estimated productivity loss (h)

  Estimating error b

  (%) Estimated productivity loss (h)

  Estimating error b

  Journal of Civil Engineering and Management, 2015, 21(7): 881–892

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  more computation time, EFSIM prediction results are significantly more accurate than competing methods. Validation results with previous studies in predicting the impact of change orders on productivity loss also indicate that EFSIM provides the smallest margin among com- peting methods. These results exhibit great potential for EFSIM as a tool to accurately predict change-order-related productivity loss. Moreover, the developed model manages to help the project manager to make an adjustment related to productivity loss caused by change order. Furthermore, this research paper succeed in demonstrating a hybrid Arti- ficial Intelligence paradigm, FL-SVM-fmGA, for facilitat- ing the decision making in the construction industry.

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